The documentary hypothesis (DH) has been the leading scholarly view on the authorship of the pentateuch since the 19th century. Fundamentalists haven't accepted it, and probably never will, but the DH has been dominany in the scholarly community for more than a century.
Nevertheless, it has faced challenges even within the scholarly community. Norman Whybray, in his 1987 book The Making of the Pentateuch, questioned many of the assumptions underlying the DH. For example, Whybray was skeptical of the idea that different names for God indicated different sources. Many religious traditions have multiple names for their deities; why should we expect ancient Judaism to be any different? Whybray also questioned what, if these sources had been kept strictly independent of each other for centuries, would motivate a redactor to combine them?
Whybray suggested that the Pentateuch was not compiled from written sources, but from fragments of oral tradition and law. An unknown author living in the 6th century BC, familiar with Greek history and mythology, decided to compile a similar history for Israel. This view, now known as the fragmentary hypothesis, has not been widely accepted by scholars, but Whybray's critiques of the DH have found a receptive audience among some European scholars.
In looking for a plausible alternative to the DH, these scholars have latched on to a view proposed in the 1970s, now known as the supplementary hypothesis. In this view, "D" (Deuteronomy) was the original source, published around 700 BC. It was then supplemented with "J" and later with "P". Under this view, there never was a distinct "E" source.
Do the challengers have a case? Although I am not a scholar, I have first-hand knowledge of how trivially easy it is to find sources that don't exist. A decade ago I wrote a satirical review of Richard Dawkins' The God Delusion, in which I "discovered" two distinct sources brought together by a skilled redactor. Today's DH scholars must take Whybray's critique seriously.
Despite the recent challenges, the documentary hypothesis still resolves more issues than any alternative, and remains the viewpoint of the majority of today's Bible scholars. And even the challengers agree that the Pentateuch wasn't written by Moses during down time in the desert. The general consensus is that Moses did not write the books associated with his name.
But does it matter?